# Could I get a longer wrench please?

A fastener is a system of 2 objects - a bolt and a nut. You come across such a bolt/nut system tightened all the way, so that the nut and the top of the bolt are pressing against each other with a force of 5 N. If the nut is held fixed, how much torque in mJ does one need to put on the bolt to begin to unscrew it?

Details and assumptions

• The radius of the bolt is $$R = 2$$ mm.
• The threads on the bolt are such that the bolt needs to rotate N = 20 cycles to move $$d = 1~cm$$ vertically away from the nut.
• The friction coefficient between the bolt and nut is $$k = 0.5$$.
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